US3598982A
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Systems for modifying functions including a convolution operation
Assignee: Mobil Oil AS
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Filing: 1967-08-08
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Granted: 1971-08-10
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Expires: 1987-08-08
Abstract
Abstract A convolution technique in which a function to be filtered is convolved with an operator of a selected character. In this manner, low-pass, high pass and band-pass type filtering or any combination thereof can be achieved. Convolution of a function which varies in amplitude along a scale with an operator including positive and negative step functions spaced along the scale will produce low-pass filtering of the function.
Inventors
- 👤 Philip L Lawrence
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-26 07:30
CPC Classifications
G; G06; G06G; G06G7/00; G06G7/12; G06G7/19; G06G7/1914
Claims Analysis
Total Claims: 12
Claim 1
Independent Claim
310 words
The method of convolving a function signal i(t), said function signal representing a quantity which varies in amplitude along a scale, with an operator signal hb h (t) -h (t) (hb h (t) -h (t) ) said method comprising the following steps each executed by automatic computing apparatus: convolving said function signal i(t) with an operator signal h (t) representing a first pair of step function signals respectively positive and negative and occurring at different positions along said scale by algebraically adding together at least two function signals, one, the integral of signal i(t) shifted along said scale by an amount indicated by one of said pair of step functions and the other, the integral of signal i(t) shifted along said scale by an amount indicated by the other of said pair of step function signals, said first pair of step function signals being respectively displaced along said scale by an amount + OR - lambda /2 from a reference point, said last-named convolving operating producing an output signal i(t)*h (t), convolving said function signal i(t) with an operator signal h (t) representing a second pair of step function signals respectively positive and negative and occurring at different positions along said scale by algebraically adding together at least two function signals, one, the integral of signal i(t) shifted along said scale by an amount indicated by one of said second pair of step functions and the other, the integral of signal i(t) shifted along said scale by an amount indicated by the other of said second pair of step function signals, said second pair of step function signals being respectively displaced along said scale by an amount + OR - lambda from a reference point, said last-named convolving operation producing an output signal i(t)*h lambda (t), and subtracting said output signal i(t)*h lambda (t) from said output signal i(t)*h (t).
Claim 2
Independent Claim
310 words
The method of convolving a function signal i(t), said function signal representing a quantity which varies in amplitude along a scale, with an operator signal hb h (t) -h (t) (hb h (t) -h (t) ) said method comprising the following steps each executed by automatic computing apparatus: convolving said function signal i(t) with an operator signal h (t) representing a first pair of step function signals respectively positive and negative and occurring at different positions along said scale by algebraically adding together at least two function signals, one, the integral of signal i(t) shifted along said scale by an amount indicated by one of said pair of step functions and the other, the integral of signal i(t) shifted along said scale by an amount indicated by the other of said pair of step function signals, said first pair of step function signals being respectively displaced along said scale by an amount + OR - lambda /2 from a reference point, said last-named convolving operating producing an output signal i(t)*h (t), convolving said function signal i(t) with an operator signal h (t) representing a second pair of step function signals respectively positive and negative and occurring at different positions along said scale by algebraically adding together at least two function signals, one, the integral of signal i(t) shifted along said scale by an amount indicated by one of said second pair of step functions and the other, the integral of signal i(t) shifted along said scale by an amount indicated by the other of said second pair of step function signals, said second pair of step function signals being respectively displaced along said scale by an amount + OR - lambda from a reference point, said last-named convolving operation producing an output signal i(t)*h lambda (t), and subtracting said output signal i(t)*h lambda (t) from said output signal i(t)*h (t).
Claim 3
Independent Claim
158 words
The method of filtering a function signal i(t) which varies in amplitude along a scale comprising the following steps each executed by automatic computing apparatus: integrating said signal i(t) to produce the function signal i(t)dt, storing the function signal i(t)dt, in a storage device for shifting said function along said scale, shifting the function signal i(t) dt along said scale by an amount lambda 2 in one direction to produce the function signal i(t+ lambda /2)dt, shifting the function signal i(t)dt along said scale in the other direction by an amount lambda /2 to produce the function signal i(t- lambda /2)dt, subtracting the function signal i(t- lambda /2)dt from the function signal i(t+ lambda /2)dt to produce the function signal i(t+ lambda /2)dt - i(t- lambda /2)dt, and normalizing said last-named function signal by multiplying said function signal by an amount proportional to 1/ lambda to produce the function signal representing low-pass filtering of said function signal i(t).
Claim 4
Independent Claim
158 words
The method of filtering a function signal i(t) which varies in amplitude along a scale comprising the following steps each executed by automatic computing apparatus: integrating said signal i(t) to produce the function signal i(t)dt, storing the function signal i(t)dt, in a storage device for shifting said function along said scale, shifting the function signal i(t) dt along said scale by an amount lambda 2 in one direction to produce the function signal i(t+ lambda /2)dt, shifting the function signal i(t)dt along said scale in the other direction by an amount lambda /2 to produce the function signal i(t- lambda /2)dt, subtracting the function signal i(t- lambda /2)dt from the function signal i(t+ lambda /2)dt to produce the function signal i(t+ lambda /2)dt - i(t- lambda /2)dt, and normalizing said last-named function signal by multiplying said function signal by an amount proportional to 1/ lambda to produce the function signal representing low-pass filtering of said function signal i(t).
Claim 5
Dependent Claim
27 words
The method recited in claim 2 further including the step of subtracting the function signal an output signal representing high pass filtering of the function signal i(t).
Claim 6
Dependent Claim
110 words
The method recited in claim 3 including the further steps of: shifting the function signal i(t)dt along said scale by an amount lambda in one direction to produce the function signal i(t+ lambda )dt, shifting the function signal i(t)dt along said scale in the other direction by an amount lambda to produce the function signal i(t- lambda )dt, subtracting the function signal i(t- lambda )dt from the function signal i(t+ lambda )dt to produce the function signal i(t+ lambda )dt - i(t- lambda )dt, normalizing said last-named function signal by multiplying the function signal by an amount proportional to 1/2 lambda to produce the function signal subtracting the function signal
Claim 7
Dependent Claim
160 words
Computing apparatus for filtering an input signal i(t) comprising: an integrator, said input signal i(t) being applied to said integrator to produce at the output thereof the signal i(t)dt, a storage unit, the signal at the output of said integrator being stored in said storage unit, means for extracting from said storage unit two components of the signal stored therein, time shifted by amounts lambda /2 and - lambda /2, said two components being the signals i(t+ lambda /2)dt and i(t- lambda /2)dt, difference means, both of said last-named signals being applied to said difference means to produce the output signal i(t+ lambda /2)dt- i(t- lambda /2)dt, and a multiplier, said last-named signal being applied to said multiplier, said multiplier being set to multiply said last-named signal by 1/ lambda to produce the output signal 1/ lambda ( i(t+ lambda /2)dt- i(t- lambda /2)dt) 1/ lambda i(t+ lambda /2)dt- i(t- lambda /2)dt representing low-pass filtering of the input signal i(t).
Claim 8
Dependent Claim
160 words
Computing apparatus for filtering an input signal i(t) comprising: an integrator, said input signal i(t) being applied to said integrator to produce at the output thereof the signal i(t)dt, a storage unit, the signal at the output of said integrator being stored in said storage unit, means for extracting from said storage unit two components of the signal stored therein, time shifted by amounts lambda /2 and - lambda /2, said two components being the signals i(t+ lambda /2)dt and i(t- lambda /2)dt, difference means, both of said last-named signals being applied to said difference means to produce the output signal i(t+ lambda /2)dt- i(t- lambda /2)dt, and a multiplier, said last-named signal being applied to said multiplier, said multiplier being set to multiply said last-named signal by 1/ lambda to produce the output signal 1/ lambda ( i(t+ lambda /2)dt- i(t- lambda /2)dt) 1/ lambda i(t+ lambda /2)dt- i(t- lambda /2)dt representing low-pass filtering of the input signal i(t).
Claim 9
Dependent Claim
51 words
The apparatus recited in claim 5 further including: means for applying the output signal 1/ lambda ( i(t+ lambda /2)dt- i(t- lambda /2)dt) 1/ lambda i(t+ lambda /2)dt- i(t-lambda /2)dt and the input signal i(t) to said difference means to produce an output representing high-pass filtering of the input signal i(t).
Claim 10
Dependent Claim
148 words
The apparatus recited in claIm 6 further including: means for extracting from said storage unit two components of the signal stored therein, time shifted by amounts proportional to lambda and - lambda , said two components being the signals i(t+ lambda )dt and i(t- lambda )dt, means for applying said last-named signals to said difference means to produce the output signal i(t+ lambda )dt- i(t-lambda )dt, said last-named output signal being applied to said multiplier which is set to 1/2 lambda to produce the output 1/2 lambda ( i(t+ lambda )dt- i(t- lambda )dt) 1/2 lambda i(t+ lambda )dt- i(t- lambda )dt , and means for applying said last-named output and the output signal 1/ lambda ( i(t+ lambda 2)dt- i(t- lambda 2)dt) 1/ lambda i(t+ lambda /2)dt- i(t- lambda /2)dt to said difference means to produce an output signal representing band-pass filtering of the input signal i(t).
Claim 11
Dependent Claim
296 words
Computing apparatus for filtering an input signal i(t) comprising: an integrator, said input signal i(t) being applied to said integrator to produce at the output thereof the signal i(t)dt, a storage unit, the signal at the output of said integrator being stored in said storage unit, means for extracting from said storage unit two components of the signal stored therein, time shifted by amounts lambda /2 and - lambda /2, said two components being the signals i(t+ lambda /2)dt and i(t- lambda /2)dt, difference means, both of said last-named signals being applied to said difference means to produce the output signal i(t+ lambda /2)dt- i(t- lambda /2)dt, a multiplier, said last-named signal being applied to said multiplier, said multiplier being set to multiply said last-named signal by 1/ lambda to produce the output signal 1/ lambda ( i(t+ lambda /2)dt- i(t- lambda /2)dt) 1/ lambda i(t+ lambda /2)dt- i(t- lambda /2)dt representing low-pass filtering of the input signal i(t), means for extracting from said storage unit two components of the signal stored therein, time shifted by amounts proportional to lambda and - lambda , said two components being the signals i(t+ lambda )dt and i(t- lambda )dt, means for applying said last-named signals to said difference means to produce the output signal i(t+ lambda )dt- i(t-lambda )dt, said last-named output signal being applied to said multiplier to produce the output 1/2 lambda ( i(t+ lambda )dt- i(t- lambda )dt) 1/2 lambda i(t+ lambda )dt- i(t- lambda )dt , and means for generating a signal representing the difference between said last-named output and the output signal 1/ lambda ( i(t+ lambda /2)dt- i(t- lambda /2)dt) 1/ lambda i(t+ lambda /2)dt- i(t- lambda /2)dt to produce an output signal and representing band-pass filtering of the input signal i(t).
Claim 12
Dependent Claim
296 words
Computing apparatus for filtering an input signal i(t) comprising: an integrator, said input signal i(t) being applied to said integrator to produce at the output thereof the signal i(t)dt, a storage unit, the signal at the output of said integrator being stored in said storage unit, means for extracting from said storage unit two components of the signal stored therein, time shifted by amounts lambda /2 and - lambda /2, said two components being the signals i(t+ lambda /2)dt and i(t- lambda /2)dt, difference means, both of said last-named signals being applied to said difference means to produce the output signal i(t+ lambda /2)dt- i(t- lambda /2)dt, a multiplier, said last-named signal being applied to said multiplier, said multiplier being set to multiply said last-named signal by 1/ lambda to produce the output signal 1/ lambda ( i(t+ lambda /2)dt- i(t- lambda /2)dt) 1/ lambda i(t+ lambda /2)dt- i(t- lambda /2)dt representing low-pass filtering of the input signal i(t), means for extracting from said storage unit two components of the signal stored therein, time shifted by amounts proportional to lambda and - lambda , said two components being the signals i(t+ lambda )dt and i(t- lambda )dt, means for applying said last-named signals to said difference means to produce the output signal i(t+ lambda )dt- i(t-lambda )dt, said last-named output signal being applied to said multiplier to produce the output 1/2 lambda ( i(t+ lambda )dt- i(t- lambda )dt) 1/2 lambda i(t+ lambda )dt- i(t- lambda )dt , and means for generating a signal representing the difference between said last-named output and the output signal 1/ lambda ( i(t+ lambda /2)dt- i(t- lambda /2)dt) 1/ lambda i(t+ lambda /2)dt- i(t- lambda /2)dt to produce an output signal and representing band-pass filtering of the input signal i(t).
References Cited (Backward Citations)
No citation records indexed.
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1974-08-09 | 1975-02-08 | 1975-08-10 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1978-08-09 | 1979-02-08 | 1979-08-10 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1982-08-09 | 1983-02-08 | 1983-08-10 | $7700.00 | Window Closed / Lapsed |